Over the years, there have been various hypotheses about the origin of the Moon. Several of them were formed before scientists had a chance to study Moon samples, and the eventual analysis (as well as calculations regarding things like energy and angular momentum) of such samples spoke against many of these old approaches.

Developed in 1878, this hypothesis by George Howard Darwin (son of Charles Darwin) states that the Moon had been a part of a rapidly spinning Earth. This rapid spin, as well as the Sun's gravitational influence, led to a piece of the Earth breaking free and forming the Moon. Osmond Fisher added that the Pacific ocean basin is actually the scar of this process.[1] Note that this was before the idea of continental drift had been raised.

Many scientists, including Édouard Roche, supported the hypothesis that the Earth and the Moon formed side by side from the material that formed all planets of this solar system. The name comes from the term "accretion disc", which is a disc formed by diffuse material that orbits a central body.[1]

For a long time, these three models had been accepted as possible lunar origins. However, later research gave a number of points that spoke against them.
After the Apollo program, rock samples taken from the Moon revealed two important things:

The Moon lacks iron. This is important to note because the Earth, in comparison, has a lot of it (in the core).

The Moon and the Earth have exactly the same oxygen isotope composition.

Along with calculations in the field of energy and angular momentum, these two points spoke against the "Big Three" hypotheses as follows:

Since the material that spun off the Earth would have come from the mantle, the lack of iron would not have been a problem (Earth's iron drained towards the core early on, leaving a depleted mantle).[2] This would also explain why the Moon has such a small core.[1] For obvious reasons, the theory also covers the issue of the oxygen isotope composition.

However, the total angular momentum today is too small to back this hypothesis.[3]

Even ignoring the very small chance of a planet easing into an Earth orbit like our Moon did, this hypothesis fails to explain the oxygen isotope similarity and also leaves open the issue of the Moon's small core.[1]

This model does not require extreme chances like the Capture theory and explains nicely why Earth and Moon share their oxygen isotope composition. However, there are open questions regarding the angular momentum, and the lack of iron spoke against it, too (It should be mentioned that this issue had been addressed recently, see Current Status.).[1]

In 1974, William Hartmann and Donald Davis suggested the hypothesis that a planetesimal (early on estimated to be the size of Mars) impacted with a relatively young Earth and blasted mantle material into orbit, where it eventually formed the Moon. This model also became known as the "Big Whack" hypothesis, because the name "Big Bang" was already taken. Around the same time, Alastair Cameron and William Ward had come to a similar conclusion. However, their research had been motivated by studies of the angular momentum.[2][4]

Initially, the hypothesis was rejected with the claim that a catastrophic event of such a dimension and with such results seemed extremely unlikely.[4] Still, it explained the lack of iron, the oxygen isotope issue and the angular momentum.

Ten years later, the Giant Impact Hypothesis emerged as the leading model after a conference about the Moon origin in Kona, Hawaii. In the 1990s, Robin Canup picked up the research and created simulations to determine possible scenarios that might explain the formation of the Moon.[2][4]

Canup initially came to the conclusion that much of the material blasted off by a "Big Whack" would either fall back to Earth or fly off into space, thus requiring a very large impactor (one with a factor of two or three in mass, compared to the initial assumptions). However, later on, improved computer simulations suggested that the size of the impactor may have been smaller after all, thus leaving all calculations regarding mass and momentum intact.[2][5]

The hypothesis is far from complete, though. Despite addressing the issues raised in the light of the first lunar landings, the Giant Impact Hypothesis leaves quite a few issues currently not fully addressed:

One study suggested three tests of the hypothesis, based on things that should have occurred after such an impact. The result of these tests did not prove the Giant Impact Hypothesis, but it also did not disprove it. Still, the paper raised a few points that have to be factored into the model.[6]

A study analysing the bulk composition has come to the conclusion that "the high bulk FeO content of the Moon rules out the derivation of the proto-lunar material from any but a small fraction of the terrestrial mantle".[7]

Addressing the above concern, the Giant Impact Hypothesis raised the point that the impactor also contributed a large share of the base material that formed the Moon. But as another paper pointed out, the Moon is lacking siderophilic elements that should be present in such a case.[8]

As of now, the Giant Impact Hypothesis still stands. Research on it is not yet complete, and the model is currently neither proven nor disproven. To date, it is the most plausible theory considered by scientists.

Independently of the Giant Impact Hypothesis, Peter Noerdlinger from Saint Mary's University in Halifax, Canada proposed an expansion of the Coaccretion model. He suggested that the Moon formed next to the Earth, complete with an iron core. But this core was then ripped out by the Earth's gravity shortly after the formation, leaving an iron-less Moon behind to orbit the Earth.[9]

Further research will show if either of these hypotheses is correct, or if scientists are going to develop a new theory based on new observations.

Alessandra Mastrobuono-Battisti and Hagai Perets from Israel Institute of Technology, Haifa, collaborating with French scientist Sean Raymond from University of Bordeaux in France, ran computer simulations which seem to show that the likelihood of collision with a large body chemically similar to the early Earth is greater than was thought.

In an interview with Space.com, astrophysicist Hagai Perets said, "The most exciting and surprising thing was to find out that we can shed new light on a 30-year-old mystery. Compositionally similar planet-impactor pairs are not rare at all."

According to Young Earth creationists, the Moon is not as old as any of the above hypotheses suggest. One argument against the commonly accepted age is that the Moon would have been lost to the pull of Earth's gravity a long time ago[11] Their current estimates put the Moon at approximately 8,000 to 10,000 years old, roughly matching the age Genesis suggests.

Both Michael Oard's "Problems for 'Giant Impact' Origin of Moon"[12] and Jonathan Sarfati's "The moon: the light that rules the night"[13] argue that evolutionists cannot explain the formation of the moon.

They're wrong,[14] not least because the origin of the Moon isn't relevant to evolution in the first place—it's a question in physics, astronomy, and geology, not biology.